As far as I know, the day of the week we choose to worship God is merely tradition, and is not actually in the bible.
The only time it is mentioned (as far as I know) is in the OT when He says we should work for 6 days, and rest on the seventh. The seventh day is Saturday.
However, because Jesus rose on the third day, Protestants traditionally worship on that day--which is a Sunday.
As a protestant, I consider myself rather conservative. However, I don't believe it makes a difference as to which day we choose, just as long as we do rest at least one day/week, and we worship and fellowship with Him.
I dopn't see what's unconservative about that. It's a convention, we worship on Sunday for the reason you stated. We all do it, no need for an innovation. Yet some people have an innate need to innovate "just because."